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A256325 a(n) = Sum_{k=0..n-1} (n-k)!*exp(-k/2)*M_{k-n,1/2}(k), where M is the Whittaker function. 1
0, 0, 1, 5, 24, 136, 933, 7589, 71376, 760796, 9051353, 118784325, 1703388648, 26486926720, 443732646029, 7965563713781, 152504645563072, 3101366761047860, 66753627906345057, 1515914174890163541, 36218232449903567992, 908098606824551207384, 23839591584412453131765 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..22.

FORMULA

a(n) = Sum_{k=0..n-1} k*(n-k)!*hypergeom([k-n+1],[2],-k).

a(n) = Sum_{k=0..n-1}(Sum_{j=0.. n-k}((n-k-j)!*C(n-k,j)*C(n-k-1,j-1)*k^j)).

MAPLE

a := n -> add(exp(-k/2)*WhittakerM(-(n-k), 1/2, k)*(n-k)!, k=0..n-1):

seq(round(evalf(a(n), 64)), n=0..22);

# Alternatively:

a := n -> add(k*(n-k)!*hypergeom([k-n+1], [2], -k), k=0..n-1):

seq(simplify(a(n)), n=0..22);

CROSSREFS

Cf. A253286.

Sequence in context: A009411 A080996 A020055 * A286743 A232318 A201952

Adjacent sequences:  A256322 A256323 A256324 * A256326 A256327 A256328

KEYWORD

nonn,easy

AUTHOR

Peter Luschny, Mar 24 2015

STATUS

approved

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Last modified November 29 14:46 EST 2020. Contains 338769 sequences. (Running on oeis4.)